Frames and Bases of Translates of Signals on Undirected Graphs
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918401352400896 |
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| author | Velsamy, Rabeetha Ramakrishnan, Radha |
| author_facet | Velsamy, Rabeetha Ramakrishnan, Radha |
| contents | We study a shift invariant space on an undirected graphs $G$ having $N$ vertices. We obtain a characterization theorem for a system of generalized translates $\{T_{i}g : 1\leq i\leq N\}$, for $g\in C^N$, to form an orthonormal basis. Moreover, we find a necessary and sufficient condition for the system $\{T_{i}g : 1\leq i\leq m\}$, $m\leq N$, to form a linearly independent set and an orthonormal set. Further, we obtain a characterization result for a system of generalized translates which is generated by multiple generators $g_{1},...,g_{M}$ to form a frame for $C^N$. In particular, we deduce similar results for the system $\{T_{i}M_{s}g : 1\leq i,s\leq N\}$ with modulation $M_{s}$ and the spectral graph wavelet system. We also provide an illustration for the spectral graph wavelet system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21026 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Frames and Bases of Translates of Signals on Undirected Graphs Velsamy, Rabeetha Ramakrishnan, Radha Classical Analysis and ODEs Signal Processing We study a shift invariant space on an undirected graphs $G$ having $N$ vertices. We obtain a characterization theorem for a system of generalized translates $\{T_{i}g : 1\leq i\leq N\}$, for $g\in C^N$, to form an orthonormal basis. Moreover, we find a necessary and sufficient condition for the system $\{T_{i}g : 1\leq i\leq m\}$, $m\leq N$, to form a linearly independent set and an orthonormal set. Further, we obtain a characterization result for a system of generalized translates which is generated by multiple generators $g_{1},...,g_{M}$ to form a frame for $C^N$. In particular, we deduce similar results for the system $\{T_{i}M_{s}g : 1\leq i,s\leq N\}$ with modulation $M_{s}$ and the spectral graph wavelet system. We also provide an illustration for the spectral graph wavelet system. |
| title | Frames and Bases of Translates of Signals on Undirected Graphs |
| topic | Classical Analysis and ODEs Signal Processing |
| url | https://arxiv.org/abs/2603.21026 |